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\/\u003E\u003C\/head\u003E\u003Cbody\u003E\u003Cdiv class=\u0022panels-ajax-tab-panel panels-ajax-tab-panel-jnl-template-cob-tab-art\u0022\u003E\u003Cdiv class=\u0022panel-display panel-1col clearfix\u0022 \u003E\n \u003Cdiv class=\u0022panel-panel panel-col\u0022\u003E\n \u003Cdiv\u003E\u003Cdiv class=\u0022panel-pane pane-highwire-markup article-heading\u0022 \u003E\n \n \n \n \u003Cdiv class=\u0022pane-content\u0022\u003E\n \u003Cdiv class=\u0022highwire-markup\u0022\u003E\u003Cdiv xmlns=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022 id=\u0022content-block-markup\u0022 data-highwire-cite-ref-tooltip-instance=\u0022highwire_reflinks_tooltip\u0022 xmlns:xhtml=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022\u003E\u003Cdiv class=\u0022article fulltext-view\u0022\u003E\u003Cspan class=\u0022highwire-journal-article-marker-start\u0022\u003E\u003C\/span\u003E\u003Cdiv class=\u0022section abstract\u0022 id=\u0022abstract-1\u0022\u003E\u003Ch2\u003ESUMMARY\u003C\/h2\u003E\n \u003Cp id=\u0022p-1\u0022\u003EThe mechanism by which surface tension allows water striders (members of\nthe genus \u003Cem\u003EGerris\u003C\/em\u003E) to stand on the surface of a pond or stream is a\nclassic example for introductory classes in animal mechanics. Until recently,\nhowever, the question of how these insects propelled themselves remained open.\nOne plausible mechanism\u2013creating momentum in the water \u003Cem\u003Evia\u003C\/em\u003E the\nproduction of capillary waves\u2013led to a paradox: juvenile water striders\nmove their limbs too slowly to produce waves, but nonetheless travel across\nthe water\u0027s surface. Two recent papers demonstrate that both water striders\nand water-walking spiders circumvent this paradox by foregoing any reliance on\nwaves to gain purchase on the water. Instead they use their legs as oars, and\nthe capillary `dimple\u0027 formed by each leg acts as the oar\u0027s blade. The\nresulting hydrodynamic drag produces vortices in the water, and the motion of\nthese vortices imparts the necessary fluid momentum. These studies pave the\nway for a more thorough understanding of the complex mechanics of walking on\nwater, and an exploration of how this intriguing form of locomotion scales\nwith the size of the organism.\u003C\/p\u003E\n \u003C\/div\u003E\u003Cul class=\u0022kwd-group KWD\u0022\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca xmlns:default=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022 href=\u0022\/search\/%20text_abstract_title%3AGerris%20text_abstract_title_flags%3Amatch-phrase%20sort%3Apublication-date\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-gerris\u0022 rel=\u0022nofollow\u0022\u003E\n \u003Cem xmlns:default=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022\u003EGerris\u003C\/em\u003E\n \u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/search\/%20text_abstract_title%3Awater%2Bstrider%20text_abstract_title_flags%3Amatch-phrase%20sort%3Apublication-date\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-water-strider\u0022 rel=\u0022nofollow\u0022\u003Ewater strider\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/search\/%20text_abstract_title%3Acapillary%2Bwave%20text_abstract_title_flags%3Amatch-phrase%20sort%3Apublication-date\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-capillary-wave\u0022 rel=\u0022nofollow\u0022\u003Ecapillary wave\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/search\/%20text_abstract_title%3ADenny%2527s%2Bparadox%20text_abstract_title_flags%3Amatch-phrase%20sort%3Apublication-date\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-dennys-paradox\u0022 rel=\u0022nofollow\u0022\u003EDenny\u0027s paradox\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/search\/%20text_abstract_title%3Aspider%20text_abstract_title_flags%3Amatch-phrase%20sort%3Apublication-date\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-spider\u0022 rel=\u0022nofollow\u0022\u003Espider\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003Cdiv class=\u0022section\u0022 id=\u0022sec-1\u0022\u003E\n \u003Ch2\u003EIntroduction\u003C\/h2\u003E\n \u003Cp id=\u0022p-2\u0022\u003EThere is something intrinsically fascinating about organisms that move\ndifferently than we do. It has been 30 years since my first course in animal\nflight, but the sight of a hummingbird hovering before a flower still causes\nme to stop and stare. Salmon leaping, snails crawling, jellyfish\npulsing\u2013when faced with the incredible variation in animal locomotion,\none can\u0027t help but gaze and wonder: how do they do that? In most cases, an\nanswer (or at least a plausible theory) is readily available, and two recent\nbook-length overviews (\u003Ca id=\u0022xref-ref-1-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-1\u0022\u003EAlexander,\n2003\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-2-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-2\u0022\u003EBiewener,\n2003\u003C\/a\u003E) go far toward scratching one\u0027s intellectual itch. All the\nmore fun, then, when the answer to the question of `how do they do that?\u0027 is\nthat no one knows. Until recently that was the situation with insects and\nspiders that walk on water.\u003C\/p\u003E\n \u003Cp id=\u0022p-3\u0022\u003EThe fascination here is actually twofold. Before one can understand how a\nwater strider can move about, one has first to explain how they can even stand\non the water\u0027s surface. In this case, the explanation is well known. First,\nthe attraction of one water molecule to another requires that considerable\nenergy be expended to create new area of air\u2013water interface. Pure water\nhas a surface energy of approximately 0.07 J m\u003Csup\u003E\u20132\u003C\/sup\u003E\n(\u003Ca id=\u0022xref-ref-4-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-4\u0022\u003EDenny, 1993\u003C\/a\u003E). Now, surface\nenergy (J m\u003Csup\u003E\u20132\u003C\/sup\u003E) is dimensionally equivalent to a capillary\ntension (N m\u003Csup\u003E\u20131\u003C\/sup\u003E), and it is in this disguise that it will be\nemployed here. Second, when a hydrophobic object is pressed into the interface\nbetween air and water, the water attempts to minimize its contact with the\nobject, often at the expense of creating new surface area. As a result, when a\nwater strider presses one of its hydrophobic legs down onto the surface of a\npond, a dimple is formed in the water\u0027s surface, and the surface is stretched\n(\u003Ca id=\u0022xref-fig-1-1\u0022 class=\u0022xref-fig\u0022 href=\u0022#F1\u0022\u003EFig. 1\u003C\/a\u003E). Thevertical component\nof the resulting capillary force resists the downward push of the leg\n(\u003Ca id=\u0022xref-fig-2-1\u0022 class=\u0022xref-fig\u0022 href=\u0022#F2\u0022\u003EFig. 2\u003C\/a\u003E), and the water strider\nis supported (e.g. \u003Ca id=\u0022xref-ref-16-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-16\u0022\u003EVogel,\n1988\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-4-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-4\u0022\u003EDenny,\n1993\u003C\/a\u003E).\u003C\/p\u003E\n \u003Cp id=\u0022p-4\u0022\u003E\n \n \u003C\/p\u003E\u003Cdiv id=\u0022F1\u0022 class=\u0022fig pos-float odd\u0022\u003E\u003Cdiv class=\u0022highwire-figure\u0022\u003E\u003Cdiv class=\u0022fig-inline-img-wrapper\u0022\u003E\u003Cdiv class=\u0022fig-inline-img\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F1.large.jpg?width=800\u0026amp;height=600\u0026amp;carousel=1\u0022 title=\u0022A water strider standing motionless on the water\u0027s surface. Note the dimples where the feet contact the water.\u0022 class=\u0022highwire-fragment fragment-images colorbox-load\u0022 rel=\u0022gallery-fragment-images-1914999897\u0022 data-figure-caption=\u0022\u0026lt;div class=\u0026quot;highwire-markup\u0026quot;\u0026gt;A water strider standing motionless on the water\u0027s surface. Note the dimples where the feet contact the water.\u0026lt;\/div\u0026gt;\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003E\u003Cspan class=\u0022hw-responsive-img\u0022\u003E\u003Cimg class=\u0022highwire-fragment fragment-image lazyload\u0022 alt=\u0022Fig. 1.\u0022 src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F1.medium.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-fragment fragment-image\u0022 alt=\u0022Fig. 1.\u0022 src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F1.medium.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cul class=\u0022highwire-figure-links inline\u0022\u003E\u003Cli class=\u0022download-fig first\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F1.large.jpg?download=true\u0022 class=\u0022highwire-figure-link highwire-figure-link-download\u0022 title=\u0022Download Fig. 1.\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload figure\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022new-tab\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F1.large.jpg\u0022 class=\u0022highwire-figure-link highwire-figure-link-newtab\u0022 target=\u0022_blank\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EOpen in new tab\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022download-ppt last\u0022\u003E\u003Ca href=\u0022\/highwire\/powerpoint\/1081151\u0022 class=\u0022highwire-figure-link highwire-figure-link-ppt\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload powerpoint\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003Cdiv class=\u0022fig-caption\u0022 xmlns:xhtml=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022\u003E\u003Cspan class=\u0022fig-label\u0022\u003EFig. 1.\u003C\/span\u003E \n \u003Cp id=\u0022p-5\u0022 class=\u0022first-child\u0022\u003EA water strider standing motionless on the water\u0027s surface. Note the\ndimples where the feet contact the water.\u003C\/p\u003E\n \u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003Cp id=\u0022p-6\u0022\u003E\n \n \u003C\/p\u003E\u003Cdiv id=\u0022F2\u0022 class=\u0022fig pos-float odd\u0022\u003E\u003Cdiv class=\u0022highwire-figure\u0022\u003E\u003Cdiv class=\u0022fig-inline-img-wrapper\u0022\u003E\u003Cdiv class=\u0022fig-inline-img\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F2.large.jpg?width=800\u0026amp;height=600\u0026amp;carousel=1\u0022 title=\u0022Surface tension (which acts parallel to the air\u0026#x2013;water interface) pulls upward on the leg of a water strider.\u0022 class=\u0022highwire-fragment fragment-images colorbox-load\u0022 rel=\u0022gallery-fragment-images-1914999897\u0022 data-figure-caption=\u0022\u0026lt;div class=\u0026quot;highwire-markup\u0026quot;\u0026gt;Surface tension (which acts parallel to the air\u0026#x2013;water interface) pulls upward on the leg of a water strider.\u0026lt;\/div\u0026gt;\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003E\u003Cspan class=\u0022hw-responsive-img\u0022\u003E\u003Cimg class=\u0022highwire-fragment fragment-image lazyload\u0022 alt=\u0022Fig. 2.\u0022 src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F2.medium.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-fragment fragment-image\u0022 alt=\u0022Fig. 2.\u0022 src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F2.medium.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cul class=\u0022highwire-figure-links inline\u0022\u003E\u003Cli class=\u0022download-fig first\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F2.large.jpg?download=true\u0022 class=\u0022highwire-figure-link highwire-figure-link-download\u0022 title=\u0022Download Fig. 2.\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload figure\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022new-tab\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F2.large.jpg\u0022 class=\u0022highwire-figure-link highwire-figure-link-newtab\u0022 target=\u0022_blank\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EOpen in new tab\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022download-ppt last\u0022\u003E\u003Ca href=\u0022\/highwire\/powerpoint\/1081153\u0022 class=\u0022highwire-figure-link highwire-figure-link-ppt\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload powerpoint\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003Cdiv class=\u0022fig-caption\u0022\u003E\u003Cspan class=\u0022fig-label\u0022\u003EFig. 2.\u003C\/span\u003E \n \u003Cp id=\u0022p-7\u0022 class=\u0022first-child\u0022\u003ESurface tension (which acts parallel to the air\u2013water interface)\npulls upward on the leg of a water strider.\u003C\/p\u003E\n \u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003Cp id=\u0022p-8\u0022\u003EThis explanation leads to a classic example of biological scaling. The\ncapillary force that supports a water strider is proportional to the perimeter\nof the legs in contact with the liquid, and therefore scales roughly in\nproportion to some linear dimension of the organism. In contrast, the weight\nof the animal (the force pushing the legs downward) is proportional to the\nanimal\u0027s volume, and therefore approximately to the cube of its linear\ndimension. In other words, with an increase in size, the tendency to sink into\nthe water increases much more rapidly than the ability to resist. As a\nconsequence, standing on water is a knack confined to small organisms. Hu et\nal. (\u003Ca id=\u0022xref-ref-11-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-11\u0022\u003E2003\u003C\/a\u003E) show that large\nwater striders have disproportionately longer legs, allowing these insects to\nreach somewhat larger sizes than we might expect. But the allometric change in\nleg length is not sufficient to completely offset the drastic increase in\nmass, and water striders are, indeed, confined to small body size.\u003C\/p\u003E\n \u003Cp id=\u0022p-9\u0022\u003EThis scaling argument has long been standard fare in introductory biology\nclasses, but in my experience, its presentation is immediately followed by a\npertinent question. Granted, small insects and spiders can stand on water, but\nhow do they move about? Early attempts at an answer led to an apparent\nparadox.\u003C\/p\u003E\n \u003C\/div\u003E\u003Cdiv class=\u0022section\u0022 id=\u0022sec-2\u0022\u003E\n \u003Ch2\u003EDenny\u0027s paradox\u003C\/h2\u003E\n \u003Cp id=\u0022p-10\u0022\u003EThe problem, at least, is intuitive. If a water strider, initially still,\nbegins to move across the surface of a pond, it gains some momentum. It can do\nso only by imparting an equal and oppositely directed momentum to it\nsurroundings, either the air or the water. Because the density of air is so\nsmall, it seems most likely that the insect moves by somehow creating momentum\nin the water. This process is familiar to anyone who has rowed a boat. The\nmass of the boat is propelled forward by the backward-directed momentum of\nwater pushed by the oars. The question, then, is how does the insect push on\nthe water?\u003C\/p\u003E\n \u003Cp id=\u0022p-11\u0022\u003EIt was at this point that the scientific study of water-strider locomotion\ninitially went astray. When faced with a basic question in locomotion, it is\noften best to start by filming the animal as it moves. Water striders can be\nbrought into the laboratory, where they busily dart about on the surface of\nwater in a shallow tray, and when lit with bright lights, their motion is\nreadily photographed. The most strikingly apparent aspect of these photographs\nis the pattern of waves that is produced each time an adult strider moves,\nwaves that move in the opposite direction from the insect. Could the momentum\nassociated with these waves be the momentum required for locomotion?\u003C\/p\u003E\n \u003Cp id=\u0022p-12\u0022\u003EThe idea has a certain appeal. The relatively large water waves with which\nwe are most familiar propagate as a result of the inertial interaction between\nthe water\u0027s mass and the restoring force of gravity. In contrast, waves with\nthe short wavelengths produced by water striders (capillary waves) move in\npart as a result of the interaction between mass and surface tension. Wouldn\u0027t\nit be lovely if the same property of water that accounted for the water\nstriders\u0027 ability to stand (surface tension), could also account for their\nability to move?\u003C\/p\u003E\n \u003Cp id=\u0022p-13\u0022\u003EThere is a problem, however. As the wavelength, \u03bb, of a pure\ncapillary wave increases, the speed of the wave, \u003Cem\u003Ec\u003C\/em\u003E\u003Csub\u003Ec\u003C\/sub\u003E, slows\ndown (see \u003Ca id=\u0022xref-ref-4-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-4\u0022\u003EDenny, 1993\u003C\/a\u003E):\n\u003Cspan class=\u0022disp-formula\u0022 id=\u0022disp-formula-1\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-1.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-1.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003Cspan class=\u0022disp-formula-label\u0022\u003E1\u003C\/span\u003E\u003C\/span\u003E\nHere \u03b3 is the surface tension of the air\u2013water interface and \u03c1\nis the water\u0027s density (approximately 1000 kg m\u003Csup\u003E\u20133\u003C\/sup\u003E). In\ncontrast, the speed of a pure gravity wave, \u003Cem\u003Ec\u003C\/em\u003E\u003Csub\u003Eg\u003C\/sub\u003E, increases\nwith an increase in wavelength:\n\u003Cspan class=\u0022disp-formula\u0022 id=\u0022disp-formula-2\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-2.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-2.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003Cspan class=\u0022disp-formula-label\u0022\u003E2\u003C\/span\u003E\u003C\/span\u003E\nwhere \u003Cem\u003E\u003Cstrong\u003Eg\u003C\/strong\u003E\u003C\/em\u003E is the acceleration of gravity, 9.81 m\ns\u003Csup\u003E\u20132\u003C\/sup\u003E. In reality, the speed of a surface wave is a combination\nof these characteristics:\n\u003Cspan class=\u0022disp-formula\u0022 id=\u0022disp-formula-3\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-3.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-3.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003Cspan class=\u0022disp-formula-label\u0022\u003E3\u003C\/span\u003E\u003C\/span\u003E\u003C\/p\u003E\n \u003Cp id=\u0022p-14\u0022\u003EThe net result of the combined influences of gravity and surface tension is\nthat there is a minimum speed at which waves can move on the surface of a\nliquid (\u003Ca id=\u0022xref-fig-3-1\u0022 class=\u0022xref-fig\u0022 href=\u0022#F3\u0022\u003EFig. 3\u003C\/a\u003E). Taking the\nderivative of \u003Ca id=\u0022xref-disp-formula-3-1\u0022 class=\u0022xref-disp-formula\u0022 href=\u0022#disp-formula-3\u0022\u003EEq. 3\u003C\/a\u003E with respect\nto wavelength and setting it equal to zero, we find that the wavelength at\nminimum speed is:\n\u003Cspan class=\u0022disp-formula\u0022 id=\u0022disp-formula-4\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-4.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-4.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003Cspan class=\u0022disp-formula-label\u0022\u003E4\u003C\/span\u003E\u003C\/span\u003E\nInserting this value into \u003Ca id=\u0022xref-disp-formula-3-2\u0022 class=\u0022xref-disp-formula\u0022 href=\u0022#disp-formula-3\u0022\u003EEq. 3\u003C\/a\u003E,\nyields the minimum wave speed:\n\u003Cspan class=\u0022disp-formula\u0022 id=\u0022disp-formula-5\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-5.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-5.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003Cspan class=\u0022disp-formula-label\u0022\u003E5\u003C\/span\u003E\u003C\/span\u003E\nFor an air\u2013water interface, this minimum speed is approximately 23 cm\ns\u003Csup\u003E\u20131\u003C\/sup\u003E. Now, in order to produce a surface wave, the object\nresponsible must be moving at least as fast as the wave it creates. Thus, the\nminimum speed of surface waves sets a minimum speed at which the leg of a\nwater strider must move in order to make waves.\u003C\/p\u003E\n \u003Cp id=\u0022p-15\u0022\u003E\n \n \u003C\/p\u003E\u003Cdiv id=\u0022F3\u0022 class=\u0022fig pos-float odd\u0022\u003E\u003Cdiv class=\u0022highwire-figure\u0022\u003E\u003Cdiv class=\u0022fig-inline-img-wrapper\u0022\u003E\u003Cdiv class=\u0022fig-inline-img\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F3.large.jpg?width=800\u0026amp;height=600\u0026amp;carousel=1\u0022 title=\u0022The speed of a pure capillary wave decreases with an increase in wavelength, while the speed of a pure gravity wave increases with an increase in wavelength. For real waves, the result is a minimum wave speed.\u0022 class=\u0022highwire-fragment fragment-images colorbox-load\u0022 rel=\u0022gallery-fragment-images-1914999897\u0022 data-figure-caption=\u0022\u0026lt;div class=\u0026quot;highwire-markup\u0026quot;\u0026gt;The speed of a pure capillary wave decreases with an increase in wavelength, while the speed of a pure gravity wave increases with an increase in wavelength. For real waves, the result is a minimum wave speed.\u0026lt;\/div\u0026gt;\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003E\u003Cspan class=\u0022hw-responsive-img\u0022\u003E\u003Cimg class=\u0022highwire-fragment fragment-image lazyload\u0022 alt=\u0022Fig. 3.\u0022 src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F3.medium.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-fragment fragment-image\u0022 alt=\u0022Fig. 3.\u0022 src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F3.medium.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cul class=\u0022highwire-figure-links inline\u0022\u003E\u003Cli class=\u0022download-fig first\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F3.large.jpg?download=true\u0022 class=\u0022highwire-figure-link highwire-figure-link-download\u0022 title=\u0022Download Fig. 3.\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload figure\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022new-tab\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F3.large.jpg\u0022 class=\u0022highwire-figure-link highwire-figure-link-newtab\u0022 target=\u0022_blank\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EOpen in new tab\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022download-ppt last\u0022\u003E\u003Ca href=\u0022\/highwire\/powerpoint\/1081155\u0022 class=\u0022highwire-figure-link highwire-figure-link-ppt\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload powerpoint\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003Cdiv class=\u0022fig-caption\u0022\u003E\u003Cspan class=\u0022fig-label\u0022\u003EFig. 3.\u003C\/span\u003E \n \u003Cp id=\u0022p-16\u0022 class=\u0022first-child\u0022\u003EThe speed of a pure capillary wave decreases with an increase in\nwavelength, while the speed of a pure gravity wave increases with an increase\nin wavelength. For real waves, the result is a minimum wave speed.\u003C\/p\u003E\n \u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003Cp id=\u0022p-17\u0022\u003ETherein lies the problem. 23 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E is a relatively high\nspeed for the leg of a small insect. For example, the middle leg of a juvenile\nwater strider may be only 2 mm long. In order for the tip of this leg to move\nat 23 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E, the leg must swing with an angular velocity of\n115 rad s\u003Csup\u003E\u20131\u003C\/sup\u003E. The entire propulsive stroke (which involves a\nrotation of about 1.5 rad) must therefore occur in about 13 ms. If the leg\ncan\u0027t rotate that fast, it can\u0027t produce waves. And if waves are the only\nmeans by which it can impart momentum to the fluid, the inability to move the\nlegs at 23 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E means that the animal can\u0027t move about.\u003C\/p\u003E\n \u003Cp id=\u0022p-18\u0022\u003EIndeed, juvenile water striders do not swing the tips of their legs at 23\ncm s\u003Csup\u003E\u20131\u003C\/sup\u003E, and they do not produce waves. They do, however,\nscamper over the water\u0027s surface just fine. This disparity between locomotory\ntheory and organismal reality (noted by briefly in\n\u003Ca id=\u0022xref-ref-4-4\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-4\u0022\u003EDenny, 1993\u003C\/a\u003E) became known as\n`Denny\u0027s paradox\u0027 (\u003Ca id=\u0022xref-ref-15-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-15\u0022\u003ESuter et al.,\n1997\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-11-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-11\u0022\u003EHu et al.,\n2003\u003C\/a\u003E).\u003C\/p\u003E\n \u003C\/div\u003E\u003Cdiv class=\u0022section\u0022 id=\u0022sec-3\u0022\u003E\n \u003Ch2\u003EThe role of a paradox\u003C\/h2\u003E\n \u003Cp id=\u0022p-19\u0022\u003EParadoxes in locomotion have often been the impetus for valuable research.\nFor example, in 1936, based on theory and measurements then available, Sir\nJames Gray calculated that the power a dolphin would expend to overcome\nhydrodynamic drag was considerably greater than the power available from its\nmuscles. `Gray\u0027s paradox\u0027 spurred decades of research on both the reduction of\ndrag by the damping of turbulent fluctuations and the energetics of mammalian\nmuscle. The current thought is that dolphins and whales have somewhat less\ndrag than Gray supposed, and that their muscles produce substantially more\npower. As our understanding improved, Gray\u0027s paradox faded away, and it is not\neven mentioned in recent texts (e.g.\n\u003Ca id=\u0022xref-ref-1-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-1\u0022\u003EAlexander, 2003\u003C\/a\u003E). Similarly, an\nengineer, Andr\u00e9 Sainte-Lagu\u00eb, used steadystate aerodynamic theory\nto calculate that bumble bees should not be able to fly\n(\u003Ca id=\u0022xref-ref-12-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-12\u0022\u003EMagnan, 1934\u003C\/a\u003E). Aside from\nmaking engineers the butt of jokes among several generations of science\nwriters (see \u003Ca id=\u0022xref-ref-5-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-5\u0022\u003EDickinson, 2001\u003C\/a\u003E),\nthe `bumblebee paradox\u0027 served as a starting point for the recent revolution\nin our understanding of insect flight. Steady-state aerodynamics indeed cannot\nexplain how a bumblebee flies (\u003Ca id=\u0022xref-ref-7-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-7\u0022\u003EEllington,\n1984\u003C\/a\u003E); an understanding of the complexities of small-scale,\nunsteady aerodynamics is necessary (e.g.\n\u003Ca id=\u0022xref-ref-8-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-8\u0022\u003EEllington et al., 1996\u003C\/a\u003E;\n\u003Ca id=\u0022xref-ref-6-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-6\u0022\u003EDickinson et al., 2000\u003C\/a\u003E).\u003C\/p\u003E\n \u003C\/div\u003E\u003Cdiv class=\u0022section\u0022 id=\u0022sec-4\u0022\u003E\n \u003Ch2\u003EParadox solved\u003C\/h2\u003E\n \u003Cp id=\u0022p-20\u0022\u003EAlthough not in the same league as Gray\u0027s paradox or the bumblebee paradox,\nDenny\u0027s paradox nonetheless tweaked the curiosity of a variety of scientists\nand engineers, and recent work suggests that it has been solved. The initial\nbreakthrough came with a study not of water striders (the organism in which\nthe paradox was framed), but rather of an oddball spider that walks on water.\nSuter et al. (\u003Ca id=\u0022xref-ref-15-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-15\u0022\u003E1997\u003C\/a\u003E) glued the\nleg of the fisher spider \u003Cem\u003EDiomedes triton\u003C\/em\u003E to a sensitive drag\ntransducer, and with the leg in its natural posture brought its tip into\ncontact with the surface of a smoothly flowing surface of water. Even though\nthe speed of the water was less than 23 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E and no waves\nwere produced, the leg encountered substantial drag. Suter and his coworkers\nhypothesized that this drag was due not to a surface phenomenon (such as\nwaves), but rather to conventional pressure drag resulting from the pattern of\nflow around the leg\u0027s dimple. By arbitrarily assuming that the drag\ncoefficient of the dimple was half that of a circular cylinder, Suter et al.\nestimated that the drag on the dimple could account for 60\u201398% of the\noverall force on the leg at velocities \u0026lt;0.2 m s\u003Csup\u003E\u20131\u003C\/sup\u003E. Suter\net al. thus solved Denny\u0027s paradox by clearly demonstrating that surface waves\nwere not the only mechanism by which an organism on the water\u0027s surface could\ncreate momentum in the water.\u003C\/p\u003E\n \u003Cp id=\u0022p-21\u0022\u003EThe study left several questions unanswered, however. Although Suter et al.\nmeasured a drag force under steady flow, they did not quantify the pattern of\nflow that was responsible. In particular, their experiments did not allow them\nto describe what happens as the leg\u0027s motion stops at the end of a rowing\nstoke. Exactly how is momentum imparted to the water? Furthermore, all their\nmeasurements were conducted at a flow speed below the critical wave speed.\nWhat happens when waves are present?\u003C\/p\u003E\n \u003Cp id=\u0022p-22\u0022\u003EThese questions served as the basis for the recent study by Hu et al.\n(\u003Ca id=\u0022xref-ref-11-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-11\u0022\u003E2003\u003C\/a\u003E). Through careful use of\nhigh-speed video and the presence of dye and particles in the water, Hu et al.\nshowed that the locomotory motion of each rowing leg of the water strider\n\u003Cem\u003EGerrus remigis\u003C\/em\u003E imparts momentum to the water through the formation of\nsurface waves, but, more importantly, also through the formation of a\nhemispherical, dipolar vortex. This unusual vortical structure can be\nvisualized as half of a typical toroidal vortex ring in which the ring has\nbeen sliced parallel to its axis of symmetry. The `cut surface\u0027 of the torus\nlies at the water\u0027s surface, and each vortex travels in the opposite direction\nfrom the water strider at a speed of approximately \u003Cem\u003EV=\u003C\/em\u003E4 cm\ns\u003Csup\u003E\u20131\u003C\/sup\u003E (\u003Ca id=\u0022xref-fig-4-1\u0022 class=\u0022xref-fig\u0022 href=\u0022#F4\u0022\u003EFig.\n4\u003C\/a\u003E)\u003C\/p\u003E\n \u003Cp id=\u0022p-23\u0022\u003E\n \n \u003C\/p\u003E\u003Cdiv id=\u0022F4\u0022 class=\u0022fig pos-float odd\u0022\u003E\u003Cdiv class=\u0022highwire-figure\u0022\u003E\u003Cdiv class=\u0022fig-inline-img-wrapper\u0022\u003E\u003Cdiv class=\u0022fig-inline-img\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F4.large.jpg?width=800\u0026amp;height=600\u0026amp;carousel=1\u0022 title=\u0022As a water strider sweeps its middle legs backward, momentum is produced in the water associated with hemispherical vortices.\u0022 class=\u0022highwire-fragment fragment-images colorbox-load\u0022 rel=\u0022gallery-fragment-images-1914999897\u0022 data-figure-caption=\u0022\u0026lt;div class=\u0026quot;highwire-markup\u0026quot;\u0026gt;As a water strider sweeps its middle legs backward, momentum is produced in the water associated with hemispherical vortices.\u0026lt;\/div\u0026gt;\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003E\u003Cspan class=\u0022hw-responsive-img\u0022\u003E\u003Cimg class=\u0022highwire-fragment fragment-image lazyload\u0022 alt=\u0022Fig. 4.\u0022 src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F4.medium.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-fragment fragment-image\u0022 alt=\u0022Fig. 4.\u0022 src=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F4.medium.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cul class=\u0022highwire-figure-links inline\u0022\u003E\u003Cli class=\u0022download-fig first\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F4.large.jpg?download=true\u0022 class=\u0022highwire-figure-link highwire-figure-link-download\u0022 title=\u0022Download Fig. 4.\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload figure\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022new-tab\u0022\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/jexbio\/207\/10\/1601\/F4.large.jpg\u0022 class=\u0022highwire-figure-link highwire-figure-link-newtab\u0022 target=\u0022_blank\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EOpen in new tab\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022download-ppt last\u0022\u003E\u003Ca href=\u0022\/highwire\/powerpoint\/1081157\u0022 class=\u0022highwire-figure-link highwire-figure-link-ppt\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload powerpoint\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003Cdiv class=\u0022fig-caption\u0022\u003E\u003Cspan class=\u0022fig-label\u0022\u003EFig. 4.\u003C\/span\u003E \n \u003Cp id=\u0022p-24\u0022 class=\u0022first-child\u0022\u003EAs a water strider sweeps its middle legs backward, momentum is produced in\nthe water associated with hemispherical vortices.\u003C\/p\u003E\n \u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003Cp id=\u0022p-25\u0022\u003EHaving visualized the flow imparted to the water by the strider, Hu et al.\neasily calculated the associated momentum. Because the vortex is approximately\nhemispherical, it volume is\n\u003Cspan class=\u0022inline-formula\u0022 id=\u0022inline-formula-1\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-6.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-6.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/span\u003E, where\n\u003Cem\u003ER\u003C\/em\u003E is the radius of the hemisphere (about 4 mm for an adult strider).\nThe mass of each vortex is thus\n\u003Cspan class=\u0022inline-formula\u0022 id=\u0022inline-formula-2\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-7.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-7.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/span\u003E,\nits momentum is \u003Cem\u003EM\u003C\/em\u003E\u003Csub\u003Ev\u003C\/sub\u003E\u003Cem\u003EV\u003C\/em\u003E, and the overall momentum\nimparted to the water by the two rowing legs is\n2\u003Cem\u003EM\u003C\/em\u003E\u003Csub\u003Ev\u003C\/sub\u003E\u003Cem\u003EV\u003C\/em\u003E, approximately 10\u003Csup\u003E\u20135\u003C\/sup\u003E kg m\ns\u003Csup\u003E\u20131\u003C\/sup\u003E. The strider itself has a mass of approximately\n10\u003Csup\u003E\u20135\u003C\/sup\u003E kg and moves at a speed of 1 m s\u003Csup\u003E\u20131\u003C\/sup\u003E, so\nit, too, has a momentum of 10\u003Csup\u003E\u20135\u003C\/sup\u003E kg m s\u003Csup\u003E\u20131\u003C\/sup\u003E. In\nother words, even when surface waves are produced (as they are by adult\nstriders) the waves account for at most a negligible fraction of the overall\nmomentum necessary for locomotion. Here, then, is conclusive proof from freely\nmoving animals that Denny\u0027s paradox can be circumvented.\u003C\/p\u003E\n \u003Cp id=\u0022p-26\u0022\u003EIn fact, the rowing locomotion of water striders appears to be quite\nefficient. When an insect of mass \u003Cem\u003EM\u003C\/em\u003E\u003Csub\u003Ei\u003C\/sub\u003E moves forward at\nspeed \u003Cem\u003EU\u003C\/em\u003E, it its body has a kinetic energy equal to\u03b3\n\u003Cem\u003EM\u003C\/em\u003E\u003Csub\u003Ei\u003C\/sub\u003E\u003Cem\u003EU\u003C\/em\u003E\u003Csup\u003E2\u003C\/sup\u003E. In terms of the animal\u0027s\nlocomotion this is `useful\u0027 energy. In the process of accelerating its body,\nhowever, the strider does work on the water. To a first approximation, this\n`wasted\u0027 energy is \u003Cem\u003EM\u003C\/em\u003E\u003Csub\u003Ev\u003C\/sub\u003E\u003Cem\u003EV\u003C\/em\u003E\u003Csup\u003E2\u003C\/sup\u003E (that is, half\nthe mass of a vortex times the square of its velocity for each of the two\nvortices). This information can be used to construct an index of the\nhydrodynamic efficiency of this form of locomotion:\n\u003Cspan class=\u0022disp-formula\u0022 id=\u0022disp-formula-6\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-8.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-8.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003Cspan class=\u0022disp-formula-label\u0022\u003E6\u003C\/span\u003E\u003C\/span\u003E\u003C\/p\u003E\n \u003Cp id=\u0022p-27\u0022\u003EA water strider with a mass of 0.01 g moves forward at 100 cm\ns\u003Csup\u003E\u20131\u003C\/sup\u003E after producing vortices with a radius of 4 mm that move\nbackwards at a velocity of 4 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E. Inserting these values\ninto \u003Ca id=\u0022xref-disp-formula-6-1\u0022 class=\u0022xref-disp-formula\u0022 href=\u0022#disp-formula-6\u0022\u003EEq. 6\u003C\/a\u003E, we find that the\nefficiency of this rowing stroke is about 96%! By utilizing vortices to propel\na large volume of water backwards at a low speed, water striders create a\nlarge amount of momentum with the expenditure of little work.\u003C\/p\u003E\n \u003C\/div\u003E\u003Cdiv class=\u0022section\u0022 id=\u0022sec-5\u0022\u003E\n \u003Ch2\u003EOpen questions\u003C\/h2\u003E\n \u003Cp id=\u0022p-28\u0022\u003EAs with most ground- (or water-)breaking studies, those of Suter et al.\n(\u003Ca id=\u0022xref-ref-15-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-15\u0022\u003E1997\u003C\/a\u003E) and Hu et al.\n(\u003Ca id=\u0022xref-ref-11-4\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-11\u0022\u003E2003\u003C\/a\u003E) lead to further\nquestions. It is now clear that water striders and aquatic spiders can row\nthemselves over the water using their legs as oar shafts and the dimples in\nthe water\u0027s surface as the oars\u0027 blades. But the shape of these blades is\nextremely dynamic. As a leg moves backward, the shape of the dimple adjusts to\nthe instantaneous force placed upon it both by the leg and by the flow\nrelative to the dimple. Whereas the shape of the static dimple can be\ndescribed accurately (see, for example,\n\u003Ca id=\u0022xref-ref-13-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-13\u0022\u003EPrincen, 1969\u003C\/a\u003E), I know of no\nattempt to account for the complex interaction among surface tension, fluid\nmomentum, viscosity and pressure that must take place in the moving dimple.\nWithout at least a description of how the shape of the dimple changes through\nthe power stroke, it is unlikely that we will be able to account for the\nprecise manner in which vortices are produced.\u003C\/p\u003E\n \u003Cp id=\u0022p-29\u0022\u003EThere is also a potential problem associated with surface tension itself.\nFor example, the dimple of a water strider\u0027s leg moving at a steady velocity\nis akin to a bubble rising through a liquid (beer, for example). In both\ncases, the pattern of flow in the liquid is due to the motion of an\nair\u2013water interface. Fluid dynamicists have long realized that this type\nof motion is unusual in that, unlike motion relative to a solid object, fluid\nmotion relative to an air\u2013water interface allows for slippage of water\nat the interface itself. For example, the theoretical drag coefficient of a\nsmall air bubble rising in water is only 2\/3 that of a buoyant sphere made\nfrom a solid material (\u003Ca id=\u0022xref-ref-10-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-10\u0022\u003EHappel and Brenner,\n1973\u003C\/a\u003E), and slippage at the air\u2013water interface may help to\nexplain why the apparent drag coefficient measured by Suter et al.\n(\u003Ca id=\u0022xref-ref-15-4\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-15\u0022\u003E1997\u003C\/a\u003E) is lower than might be\nexpected. Furthermore, there can be discrepancies between the theoretical drag\ncoefficient for a bubble and that measured in an actual fluid. Small bubbles\nrising in beer move slower than simple theory predicts; instead, they act as\nif the air\u2013water interface has some `stiffness\u0027\n(\u003Ca id=\u0022xref-ref-10-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-10\u0022\u003EHappel and Brenner, 1973\u003C\/a\u003E).\nThe apparent solidity of the bubble\u0027s surface may be due to surface-active\nagents in the interface. As these molecules are swept back by the flow, they\ncan accumulate at the downstream end of the bubble, and thereby resist\nslippage in much the same fashion as the surface of a solid. One supposes that\nsurface-active molecules might accumulate along the surface upstream of a\nwater strider\u0027s leg, thereby affecting the flow. Alternatively, in 1913\nBoussinesq (as cited in \u003Ca id=\u0022xref-ref-10-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-10\u0022\u003EHappel and\nBrenner, 1973\u003C\/a\u003E) pointed out that surface tension is a static\nproperty of a fluid, and therefore it may be inappropriate to use it to\nexplain dynamic processes such as flow around a bubble or dimple. Building on\nthis thought, Boussinesq explained the anomalous motion of small bubbles by\nhypothesizing that under nonsteady flow (and even in the absence of\nsurface-active molecules), an air\u2013water interface can exhibit an\nintrinsic elasticity. I should note that bubbles rising in beer are smaller\nthan the leg dimples of water striders and move at a substantially slower\nspeed [that is, they have a lower Reynolds number (see below)], but the issue\nof slippage at the air\u2013water interface and the possibility of surface\nelasticity may nonetheless have important consequences for any attempt to\nprecisely model the drag acting on the leg of a water strider or spider.\u003C\/p\u003E\n \u003Cp id=\u0022p-30\u0022\u003EThere is also much to be learned about the scaling of surface locomotion.\nHu et al. (\u003Ca id=\u0022xref-ref-11-5\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-11\u0022\u003E2003\u003C\/a\u003E) note that in\norder for vortices to be shed from the leg of a water strider, the Reynolds\nnumber of the dimple must be greater than approximately 100. As suggested by\nHu et al., one can calculate Reynolds number using \u003Cem\u003EL\u003C\/em\u003E, the length of\nthe distal segment of the leg (the tarsus), as an estimate of the flow-wise\ndimension of the dimple:\n\u003Cspan class=\u0022disp-formula\u0022 id=\u0022disp-formula-7\u0022\u003E\u003Cspan class=\u0022highwire-responsive-lazyload\u0022\u003E\u003Cimg src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 class=\u0022highwire-embed tex lazyload\u0022 alt=\u0022Math\u0022 data-src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-9.gif\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-embed tex\u0022 alt=\u0022Math\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/highwire\/jexbio\/207\/10\/1601\/embed\/tex-math-9.gif\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003Cspan class=\u0022disp-formula-label\u0022\u003E7\u003C\/span\u003E\u003C\/span\u003E\u003C\/p\u003E\n \u003Cp id=\u0022p-31\u0022\u003EHere \u003Cem\u003Eu\u003C\/em\u003E is the speed of the dimple over the water (which we\napproximate using the velocity of the rowing leg relative to the insect\u0027s\nbody) and \u03bd is the kinematic viscosity of water (approximately\n10\u003Csup\u003E\u20136\u003C\/sup\u003E m\u003Csup\u003E2\u003C\/sup\u003E s\u003Csup\u003E\u20131\u003C\/sup\u003E for pure water). If\nRe \u0026gt;100, the product of tarsus length and leg velocity must therefore\nexceed approximately 10\u003Csup\u003E\u20134\u003C\/sup\u003E m\u003Csup\u003E2\u003C\/sup\u003E s\u003Csup\u003E\u20131\u003C\/sup\u003E.\nGiven that smaller bugs are likely to have both smaller legs and slower\nvelocities, this relationship potentially places a severe lower limit on the\neffective size of water striders. If the animals are too small, they cannot\nmove their legs fast enough to create either vortices or surface waves, and\nthey therefore are unlikely to be able to move. Exactly where this limit\noccurs depends on the scaling of leg length and angular velocity in surface\ninsects, as well as on a more precise determination of the critical Reynolds\nnumber that must be exceeded if vortices are to be shed.\u003C\/p\u003E\n \u003Cp id=\u0022p-32\u0022\u003EWe have seen that surface tension sets a maximal size at which animals can\nsupport themselves on water; if they get too big, they sink. Vortex shedding\nis likely to set the minimal size, a limit that appears to fall just below the\nsize of the smallest juvenile water striders. There are other limitations as\nwell. For example, Suter and Wildman\n(\u003Ca id=\u0022xref-ref-14-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-14\u0022\u003E1999\u003C\/a\u003E) have shown that \u003Cem\u003ED.\ntriton\u003C\/em\u003E, the water-walking spider, changes its gait from a rowing motion\n(of the same sort used by water striders) to a galloping motion as its speed\nincreases. They propose that the change in gait occurs when the rowing legs\nexceed the speed at which surface tension can maintain the integrity of the\nsurface dimple. Above this critical speed, the legs are stabbed vertically\ninto the water, incurring no appreciable dimple, and the legs subsequently act\nas simple oars, relying on the drag of the leg alone.\u003C\/p\u003E\n \u003Cp id=\u0022p-33\u0022\u003ETo fully understand this gait transition, we again need to be able to\naccount for the complex dynamics of the leg\u0027s surface dimple, and precise\nanswers are therefore unavailable. We can, however, make a rough guess as to\nthe critical speed. Batchelor\n(\u003Ca id=\u0022xref-ref-3-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-3\u0022\u003E1967\u003C\/a\u003E) suggests that bubbles\nrising in a liquid begin to deform from their spherical shape if the dynamic\npressure of the flow (\u03b3\u03c1\u003Cem\u003Eu\u003C\/em\u003E\u003Csup\u003E2\u003C\/sup\u003E) is a substantial\nfraction of the pressure increase that surface tension imposes across the\nair\u2013water interface. In turn, the magnitude of the pressure increase is\ninversely related to the local curvature of the interface, which,\nunfortunately, we do not know for the dynamic dimple of a moving water\nstrider. For the sake of argument, let us assume that the radius of curvature\nof the dimple is approximately equal to \u003Cem\u003Er\u003C\/em\u003E, the radius of the tarsus.\nThe resulting surface-tension-induced pressure is \u03b3\/\u003Cem\u003Er\u003C\/em\u003E\n(\u003Ca id=\u0022xref-ref-4-5\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-4\u0022\u003EDenny, 1993\u003C\/a\u003E). For a tarsus 1\nmm in radius (such as that of the spiders used by\n\u003Ca id=\u0022xref-ref-14-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-14\u0022\u003ESuter and Wildman, 1999\u003C\/a\u003E), this\nimplies that the dynamic pressure is equal to the surface-tension-induced\npressure at a velocity of 38 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E. We might therefore\nexpect that the dimple will become unstable at velocities somewhat slower than\nthis. Indeed, Suter and Wildman\n(\u003Ca id=\u0022xref-ref-14-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-14\u0022\u003E1999\u003C\/a\u003E) showed that the maximum\nleg-tip velocity in a rowing spider was about 30 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E.\nWater striders have tarsi with smaller radii (approximately 40 \u03bcm),\nimplying that their legs must move at 191 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E before the\ndynamic pressure is equal to the surface-tension pressure. Hu et al.\n(\u003Ca id=\u0022xref-ref-11-6\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-11\u0022\u003E2003\u003C\/a\u003E) recorded leg velocities\nof 100 cm s\u003Csup\u003E\u20131\u003C\/sup\u003E with no evidence that the dimple had become\nunstable.\u003C\/p\u003E\n \u003Cp id=\u0022p-34\u0022\u003ESo, one more locomotory paradox bites the dust, but interesting questions\nremain before the question of `how do they do that?\u0027 is fully resolved. For\nthe time being, my curiosity will continue to itch.\u003C\/p\u003E\n \u003C\/div\u003E\u003Cdiv class=\u0022section ack\u0022 id=\u0022ack-1\u0022\u003E\u003Ch2\u003EACKNOWLEDGEMENTS\u003C\/h2\u003E\n \u003Cp id=\u0022p-35\u0022\u003EThanks to Charlie Ellington, Robert Dudley and Michael Dickinson for their\nhelp in tracking down the origin of the bumblebee paradox.\u003C\/p\u003E\n \u003C\/div\u003E\u003Cul class=\u0022copyright-statement\u0022\u003E\u003Cli class=\u0022fn\u0022 id=\u0022copyright-statement-1\u0022\u003E\u00a9 The Company of Biologists Limited\n2004\u003C\/li\u003E\u003C\/ul\u003E\u003Cdiv class=\u0022section ref-list\u0022 id=\u0022ref-list-1\u0022\u003E\u003Ch2\u003EReferences\u003C\/h2\u003E\u003Col class=\u0022cit-list ref-use-labels\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-1-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-1\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.1\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EAlexander, R. McN.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E2003\u003C\/span\u003E).\n\u003Cspan class=\u0022cit-source\u0022\u003EPrinciples of Animal Locomotion\u003C\/span\u003E. Princeton: Princeton\nUniversity Press.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-2-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-2\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.2\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EBiewener, A. A.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E2003\u003C\/span\u003E). \u003Cspan class=\u0022cit-source\u0022\u003EAnimal\nLocomotion\u003C\/span\u003E. Oxford: Oxford University Press.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-3-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-3\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.3\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EBatchelor, G. K.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1967\u003C\/span\u003E). \u003Cspan class=\u0022cit-source\u0022\u003EAn\nIntroduction to Fluid Dynamics\u003C\/span\u003E. Cambridge: Cambridge University\nPress.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-4-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-4\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.4\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EDenny, M. W.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1993\u003C\/span\u003E). \u003Cspan class=\u0022cit-source\u0022\u003EAir and\nWater\u003C\/span\u003E. Princeton: Princeton University Press.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-5-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-5\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.5\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EDickinson, M.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E2001\u003C\/span\u003E). Solving the mystery of\ninsect flight. \u003Cspan class=\u0022cit-source\u0022\u003ESci. Am.\u003C\/span\u003E\n\u003Cspan class=\u0022cit-vol\u0022\u003E284\u003C\/span\u003E, \u003Cspan class=\u0022cit-fpage\u0022\u003E49\u003C\/span\u003E-57.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DSci.%2BAm.%26rft.volume%253D284%26rft.spage%253D49%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-6-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-6\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.6\u0022 data-doi=\u002210.1126\/science.288.5463.100\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EDickinson, M. et al.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E2000\u003C\/span\u003E).\n\u003Cspan class=\u0022cit-source\u0022\u003EScience\u003C\/span\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E288\u003C\/span\u003E,\u003Cspan class=\u0022cit-fpage\u0022\u003E100\u003C\/span\u003E\n-106.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DScience%26rft.stitle%253DScience%26rft.issn%253D0036-8075%26rft.aulast%253DDickinson%26rft.auinit1%253DM.%2BH.%26rft.volume%253D288%26rft.issue%253D5463%26rft.spage%253D100%26rft.epage%253D106%26rft.atitle%253DHow%2BAnimals%2BMove%253A%2BAn%2BIntegrative%2BView%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fscience.288.5463.100%26rft_id%253Dinfo%253Apmid%252F10753108%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Mzoic2NpIjtzOjU6InJlc2lkIjtzOjEyOiIyODgvNTQ2My8xMDAiO3M6NDoiYXRvbSI7czoyNDoiL2pleGJpby8yMDcvMTAvMTYwMS5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-7-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-7\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.7\u0022 data-doi=\u002210.1098\/rstb.1984.0049\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EEllington, C. P.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1984\u003C\/span\u003E). The aerodynamics of\nhovering flight: I. The quasisteady analysis. \u003Cspan class=\u0022cit-source\u0022\u003EPhil. Trans. R. Soc.\nB\u003C\/span\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E305\u003C\/span\u003E,\u003Cspan class=\u0022cit-fpage\u0022\u003E1\u003C\/span\u003E\n-15.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DPhilosophical%2BTransactions%2Bof%2Bthe%2BRoyal%2BSociety%2BB%253A%2BBiological%2BSciences%26rft.stitle%253DPhil%2BTrans%2BR%2BSoc%2BB%26rft.issn%253D0080-4622%26rft.aulast%253DEllington%26rft.auinit1%253DC.%2BP.%26rft.volume%253D305%26rft.issue%253D1122%26rft.spage%253D1%26rft.epage%253D15%26rft.atitle%253DThe%2BAerodynamics%2Bof%2BHovering%2BInsect%2BFlight.%2BI.%2BThe%2BQuasi-Steady%2BAnalysis%26rft_id%253Dinfo%253Adoi%252F10.1098%252Frstb.1984.0049%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Njoicm95cHRiIjtzOjU6InJlc2lkIjtzOjEwOiIzMDUvMTEyMi8xIjtzOjQ6ImF0b20iO3M6MjQ6Ii9qZXhiaW8vMjA3LzEwLzE2MDEuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-8-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-8\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.8\u0022 data-doi=\u002210.1038\/384626a0\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EEllington, C. P., van den Berg, C., Willmott, A. P. and Thomas,\nA. I.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1996\u003C\/span\u003E). Leading-edge vortices in insect flight.\n\u003Cspan class=\u0022cit-source\u0022\u003ENature\u003C\/span\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E384\u003C\/span\u003E,\u003Cspan class=\u0022cit-fpage\u0022\u003E626\u003C\/span\u003E\n-630.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DNature%26rft.volume%253D384%26rft.spage%253D626%26rft_id%253Dinfo%253Adoi%252F10.1038%252F384626a0%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1038\/384626a0\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=A1996VZ29600029\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other no-rev-xref\u0022 id=\u0022cit-207.10.1601.9\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EGray, J.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1936\u003C\/span\u003E). Studies in animal locomotion\nVI. The propulsive power of the dolphin. \u003Cspan class=\u0022cit-source\u0022\u003EJ. Exp. Biol.\u003C\/span\u003E\n\u003Cspan class=\u0022cit-vol\u0022\u003E13\u003C\/span\u003E,\u003Cspan class=\u0022cit-fpage\u0022\u003E192\u003C\/span\u003E\n-199.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DJournal%2Bof%2BExperimental%2BBiology%26rft.stitle%253DJ.%2BExp.%2BBiol.%26rft.issn%253D0022-0949%26rft.aulast%253DGRAY%26rft.auinit1%253DJ.%26rft.volume%253D13%26rft.issue%253D2%26rft.spage%253D192%26rft.epage%253D199%26rft.atitle%253DStudies%2Bin%2BAnimal%2BLocomotion%253A%2BVI.%2BThe%2BPropulsive%2BPowers%2Bof%2Bthe%2BDolphin%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6NjoiamV4YmlvIjtzOjU6InJlc2lkIjtzOjg6IjEzLzIvMTkyIjtzOjQ6ImF0b20iO3M6MjQ6Ii9qZXhiaW8vMjA3LzEwLzE2MDEuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-10-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-10\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.10\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EHappel, J. and Brenner, H.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1973\u003C\/span\u003E).\u003Cspan class=\u0022cit-source\u0022\u003E\u003Cem\u003ELow Reynolds Number Hydrodynamics\u003C\/em\u003E (second edition)\u003C\/span\u003E\n.\nDordrecht: Kluwer Academic Publishers.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-11-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-11\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.11\u0022 data-doi=\u002210.1038\/nature01793\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EHu, D. L., Chan, B. and Bush, J. W. M.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E2003\u003C\/span\u003E).\nThe hydrodynamics of water strider locomotion. \u003Cspan class=\u0022cit-source\u0022\u003ENature\u003C\/span\u003E\n\u003Cspan class=\u0022cit-vol\u0022\u003E424\u003C\/span\u003E,\u003Cspan class=\u0022cit-fpage\u0022\u003E663\u003C\/span\u003E\n-666.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DNature%26rft.stitle%253DNature%26rft.issn%253D0028-0836%26rft.aulast%253DHu%26rft.auinit1%253DD.%2BL.%26rft.volume%253D424%26rft.issue%253D6949%26rft.spage%253D663%26rft.epage%253D666%26rft.atitle%253DThe%2Bhydrodynamics%2Bof%2Bwater%2Bstrider%2Blocomotion.%26rft_id%253Dinfo%253Adoi%252F10.1038%252Fnature01793%26rft_id%253Dinfo%253Apmid%252F12904790%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1038\/nature01793\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=12904790\u0026amp;link_type=MED\u0026amp;atom=%2Fjexbio%2F207%2F10%2F1601.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000184578800042\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-12-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-12\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.12\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EMagnan, A.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1934\u003C\/span\u003E). \u003Cspan class=\u0022cit-source\u0022\u003ELe Vol des\nInsects\u003C\/span\u003E\u003Cem\u003E.\u003C\/em\u003E Paris: Hermann et Cie, Publishers.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-13-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-13\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.13\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EPrincen, H. M.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1969\u003C\/span\u003E). The equilibrium shapes\nof interfaces, drops, and bubbles: Rigid and deformable particles at\ninterfaces. \u003Cspan class=\u0022cit-source\u0022\u003ESurface Colloid Sci.\u003C\/span\u003E\n\u003Cspan class=\u0022cit-vol\u0022\u003E2\u003C\/span\u003E, \u003Cspan class=\u0022cit-fpage\u0022\u003E1\u003C\/span\u003E-84.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-14-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-14\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.14\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003ESuter, R. B. and Wildman, H.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1999\u003C\/span\u003E). Locomotion\non the water surface: hydrodynamic constraints on rowing velocity require a\ngait change. \u003Cspan class=\u0022cit-source\u0022\u003EJ. Exp. Biol.\u003C\/span\u003E\n\u003Cspan class=\u0022cit-vol\u0022\u003E202\u003C\/span\u003E,\u003Cspan class=\u0022cit-fpage\u0022\u003E2771\u003C\/span\u003E\n-2785.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DJournal%2Bof%2BExperimental%2BBiology%26rft.stitle%253DJ.%2BExp.%2BBiol.%26rft.issn%253D0022-0949%26rft.aulast%253DSuter%26rft.auinit1%253DR.%26rft.volume%253D202%26rft.issue%253D20%26rft.spage%253D2771%26rft.epage%253D2785%26rft.atitle%253DLocomotion%2Bon%2Bthe%2Bwater%2Bsurface%253A%2Bhydrodynamic%2Bconstraints%2Bon%2Browing%2Bvelocity%2Brequire%2Ba%2Bgait%2Bchange%26rft_id%253Dinfo%253Apmid%252F10504313%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6NjoiamV4YmlvIjtzOjU6InJlc2lkIjtzOjExOiIyMDIvMjAvMjc3MSI7czo0OiJhdG9tIjtzOjI0OiIvamV4YmlvLzIwNy8xMC8xNjAxLmF0b20iO31zOjg6ImZyYWdtZW50IjtzOjA6IiI7fQ==\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-15-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-15\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.15\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003ESuter, R. B., Rosenberg, O., Loeb, S., Wildman, H. and Long,\nJ.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1997\u003C\/span\u003E). Locomotion on the water surface: propulsive\nmechanisms of the fisher spider \u003Cem\u003EDolomeds triton. \u003C\/em\u003E\u003Cspan class=\u0022cit-source\u0022\u003EJ. Exp.\nBiol.\u003C\/span\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E200\u003C\/span\u003E,\u003Cspan class=\u0022cit-fpage\u0022\u003E2523\u003C\/span\u003E\n-2538.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DJournal%2Bof%2BExperimental%2BBiology%26rft.stitle%253DJ.%2BExp.%2BBiol.%26rft.issn%253D0022-0949%26rft.aulast%253DSuter%26rft.auinit1%253DR.%26rft.volume%253D200%26rft.issue%253D19%26rft.spage%253D2523%26rft.epage%253D2538%26rft.atitle%253DLocomotion%2Bon%2Bthe%2Bwater%2Bsurface%253A%2Bpropulsive%2Bmechanisms%2Bof%2Bthe%2Bfisher%2Bspider%26rft_id%253Dinfo%253Apmid%252F9320450%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6NjoiamV4YmlvIjtzOjU6InJlc2lkIjtzOjExOiIyMDAvMTkvMjUyMyI7czo0OiJhdG9tIjtzOjI0OiIvamV4YmlvLzIwNy8xMC8xNjAxLmF0b20iO31zOjg6ImZyYWdtZW50IjtzOjA6IiI7fQ==\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-16-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-16\u0022\u003E\u21b5\u003C\/a\u003E\n \u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-207.10.1601.16\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Ccite\u003E\u003Cstrong\u003EVogel, S.\u003C\/strong\u003E (\u003Cspan class=\u0022cit-pub-date\u0022\u003E1988\u003C\/span\u003E). \u003Cspan class=\u0022cit-source\u0022\u003ELife\u0027s\nDevices\u003C\/span\u003E. Princeton: Princeton University Press.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\n \u003C\/li\u003E\u003C\/ol\u003E\u003C\/div\u003E\u003Cspan class=\u0022highwire-journal-article-marker-end\u0022\u003E\u003C\/span\u003E\u003C\/div\u003E\u003Cspan id=\u0022related-urls\u0022\u003E\u003C\/span\u003E\u003C\/div\u003E\u003Ca href=\u0022http:\/\/jeb.biologists.org\/content\/207\/10\/1601.abstract\u0022 class=\u0022hw-link hw-link-article-abstract\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EView Abstract\u003C\/a\u003E\u003C\/div\u003E \u003C\/div\u003E\n\n \n \u003C\/div\u003E\n\u003Cdiv class=\u0022panel-separator\u0022\u003E\u003C\/div\u003E\u003Cdiv class=\u0022panel-pane pane-highwire-article-trendmd\u0022 \u003E\n \n \n \n \u003Cdiv class=\u0022pane-content\u0022\u003E\n \u003Cdiv id=\u0022trendmd-suggestions\u0022\u003E\u003C\/div\u003E \u003C\/div\u003E\n\n \n \u003C\/div\u003E\n\u003C\/div\u003E\n \u003C\/div\u003E\n\u003C\/div\u003E\n\u003C\/div\u003E\u003Cscript type=\u0022text\/javascript\u0022 src=\u0022http:\/\/jeb.biologists.org\/sites\/default\/files\/js\/js_sV49gyv9i81wi195EDEJAEugofQ6ixO-urBJ5CiQPjw.js\u0022\u003E\u003C\/script\u003E\n\u003C\/body\u003E\u003C\/html\u003E"}